scholarly journals Experimental Study on Fragmentation Behavior of Specimen with Rockbolts

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Enyuan Dong ◽  
Weijun Wang ◽  
Zhiwei Zhao ◽  
Wenqing Peng ◽  
Chao Yuan
Keyword(s):  
Fractal Dimension ◽  
Quantitative Description ◽  
Fractal Dimensions ◽  
Surrounding Rock ◽  
Distribution Law ◽  
Support Mechanism ◽  
Fragmentation Behavior ◽  
Surface Fractal ◽  
Average Size ◽  
Degree Of Fragmentation

The effect of rockbolt density on fractured specimens and the distribution law of fragments were studied using the fractal method. The results show that with the increase of rockbolt density, the strength of specimens is improved. Its degree of fragmentation is increased, but the average size of fragments is decreased. The fragmentation and surface fractal dimensions are increased, their difference value is 1 in theory, but the value is slightly less than 1 in practical application due to the uncertain factors such as anisotropy of specimen. There is a positive correlation between the deformation of surrounding rock and its fractal dimension. The surface fractal dimension of surrounding rock can give a quantitative description of its degree of fragmentation and can give a comprehensive reflection to the roof stability. The support mechanism of rockblots can be understood as improving the probability of refragmentation of fragments, making its distribution gradation close to the optimal one with minimum porosity, thus reducing the deformation of surrounding rock.

Characterizing Woodiness Carbon Fiber Precursor by Fractal Geometry Approach in Different Curing Conditions

2013 ◽  
Vol 710 ◽  
pp. 122-126
Author(s):  
Zhi Gao Liu ◽  
Qiu Hui Zhang ◽  
Guang Jie Zhao ◽  
Lu Zhang
Keyword(s):  
Fractal Dimension ◽  
Carbon Fiber ◽  
Fractal Dimensions ◽  
Morphological Characters ◽  
Curing Conditions ◽  
Surface Fractal ◽  
Dimension Measurement ◽  
Microscopy Image ◽  
Calculation System ◽  
Carbon Fiber Precursor

For exploring the variation of the surface morphology of carbon fiber precursor which was obtained from different curing conditions,this paper used the fractal dimension measurement method to analyze morphological characters of carbon fiber precursor surface through the electronic scanning electron microscopy image recognition and computer fractal calculation system. The experimental results show:the surface fractal dimensions of carbon fiber precursor were between 2.480~2.622 by TPSAM method, and the surface fractal dimensions of carbon fiber precursor were between 2.555~2.633 by PCM method, both methods show that the carbon fiber precursor surface is smooth. And the CCM is 2.678~2.755, this method shows that the precursor surface is concave and convex. The fractal dimension value obtained by TPSAM method and PCM method is closer, while the CCM is different. But the trend is almost the same, which shows that using the fractal dimension method to desirable the surface structure of carbon fiber precursor is desirable.

A Microcontact Model Developed for Asperity Heights With a Variable Profile Fractal Dimension, a Surface Fractal Dimension, Topothesy, and Non-Gaussian Distribution

2008 ◽  
Author(s):  
Jen Luen Liou ◽  
Jen Fin Lin
Keyword(s):  
Fractal Dimension ◽  
Cross Sections ◽  
Fractal Dimensions ◽  
Surface Fractal Dimension ◽  
Surface Fractal ◽  
Deformation Regime ◽  
Circular Contour ◽  
The Mean ◽  
Non Gaussian ◽  
The Relationship

The cross sections formed by the contact asperities of two rough surfaces at an interference are island-shaped, rather than having the commonly assumed circular contour. These island-shaped contact surface contours show fractal behavior with a profile fractal dimension Ds. The surface fractal dimension for the asperity heights is defined as D and the topothesy is defined as G. In the study of Mandelbrot, the relationship between D and Ds was given as D = Ds+1 if these two fractal dimensions are obtained before contact deformation. In the present study, D, G, and Ds are considered to be varying with the mean separation (or the interference at the rough surface) between two contact surfaces. The D-Ds relationships for the contacts at the elastic, elastoplastic, and fully plastic deformations are derived and the inceptions of the elastoplastic deformation regime and the fully plastic deformation regime are redefined using the equality of two expressions established in two different ways for the number of contact spots (N).

scholarly journals TECHNIQUE FOR DETERMINATION OF SURFACE FRACTAL DIMENSION AND MORPHOLOGY OF MESOPOROUS TITANIA USING DYNAMIC FLOW ADSORPTION AND ITS CHARACTERIZATION

2010 ◽  
Vol 9 (1) ◽  
pp. 13-17
Author(s):  
Silvester Tursiloadi
Keyword(s):  
Fractal Dimension ◽  
Adsorption Isotherm ◽  
Surface Morphology ◽  
Average Pore Size ◽  
Fractal Dimensions ◽  
Nano Particles ◽  
Dynamic Flow ◽  
N2 Adsorption ◽  
Surface Fractal Dimension ◽  
Surface Fractal

A technique to determine the surface fractal dimension of mesoporous TiO­2 using a dynamic flow adsorption instrument is described. Fractal dimension is an additional technique to characterize surface morphology. Surface fractal dimension, a quantitative measurement of surface ruggedness, can be determined by adsorbing a homologous series of adsorbates onto an adsorbent sample of mesoporous TiO­2. Titania wet gel prepared by hydrolysis of Ti-alkoxide was immersed in the flow of supercritical CO2 at 60 °C and the solvent was extracted.  Mesoporous TiO­2 consists of anatase nano-particles, about 5nm in diameter, have been obtained. After calcination at 600 °C, the average pore size of the extracted gel, about 20nm in diameter, and the pore volume, about 0.35cm3g-1, and the specific surface area, about 58 m2g-1. Using the N2 adsorption isotherm, the surface fractal dimension, DS, has been estimated according to the Frenkel-Halsey-Hill (FHH) theory. The N2 adsorption isotherm for the as-extracted aerogel indicates the mesoporous structure. Two linear regions are found for the FHH plot of the as-extracted aerogel. The estimated surface fractal dimensions are about 2.49 and 2.68. Both of the DS  values indicate rather complex surface morphology. The TEM observation shows that there are amorphous and crystalline particles. Two values of DS may be attributed to these two kinds of particles. The two regions are in near length scales, and the smaller DS, DS =2.49, for the smaller region. This result indicates that there are two kinds of particles, probably amorphous and anatase particles as shown by the TEM observation.     Keywords: surface fractal dimensions, CO2 supercritically extraction, sol-gel, aerogel, titania

Study and Elucidation of Fractal Dimension in Anionic and Cationic Clays: Relationship between Fractal Dimensions to the Amount Adsorbed and Pore Size

2018 ◽  
Vol 30 ◽  
pp. 25-42
Author(s):  
Salah Bahah ◽  
Saci Nacef ◽  
Derradji Chebli ◽  
Brahim Djellouli ◽  
Abdallah Bouguettoucha
Keyword(s):  
Fractal Dimension ◽  
Zeta Potential ◽  
Fractal Dimensions ◽  
Molar Ratio ◽  
Relative Pressure ◽  
Hill Model ◽  
Heterogeneous Distribution ◽  
Anionic Clays ◽  
Surface Fractal ◽  
Bet Analysis

In order to search the correlation between textural properties and geometrical heterogeneity in clays, as characterized by the surface fractal dimension, we used, three different cationic clays; namely Kaolin of Hamam Dbagh, Montmorillonite (Mt) of Maghnia and a sample prepared from Sodium Montmorillonte (Na-Mt)) and three different synthetic anionic clays, ZnAlCO3, MgAlCO3at a molar ratio equal to three (R=3), and NiAlCO3with different molar ratios (R=2, R=3 and R= 4). This DSparameter was evaluated from nitrogen (N2) analysis gas. the fractal Frenkel-Halsey-Hill (FHH) (DS) models was used to estimate the surface fractal dimensions at two ranges of relative pressure, the first between 0.08 and 0.22, which were found Ds to be 2.59, 2.53 and 2.68 from Kaolin, Montmorillonite and Sodium Montmorillonte clays respectively and 2.33, 2.61, 2.53, 2.56 and 2.56 for ZnAlCO3and MgAlCO3, NiAlCO3(2, 3 and 4) respectively, and other at medium relative pressure, which there was an excellent linear adjustment for F-H-H equation within the range between 0.37 and 0.82, which were found Ds to be 2.77, 2.64 and 2.82 for Kaolinite, Montmorillonite and Sodium Montmorillonte clays respectively, and 2.68, 2.64, 2.40, 2.60, 2.47 for ZnAlCO3, MgAlCO3, NiAlCO3(2, 3 and 4) respectively. SEM Characterization confirmed the heterogeneous distribution of the particles and the BET analysis confirmed the fractal nature of the surface of these materials. The zeta potential of the sample which is most used as an indicator of dispersion stability, show a proportionality between increases of zeta potential with increase of dimension fractal (DS), for the same type of clays ( (NiAlCO3) with (R=2, 3 and 4) and Mt, Na-Mt). Key words: Anionic clays; Cationic clays; Fractal dimension; geometrical heterogeneity; Frenkel-Halsey-Hill model.

scholarly journals Fractal analysis of bentonite modified with heteropoly acid using nitrogen sorption and mercury intrusion porosimetry

2011 ◽  
Vol 76 (10) ◽  
pp. 1403-1410 ◽  
Author(s):  
Srdjan Petrovic ◽  
Zorica Vukovic ◽  
Tatjana Novakovic ◽  
Zoran Nedic ◽  
Ljiljana Rozic
Keyword(s):  
Fractal Dimension ◽  
Specific Surface ◽  
Surface Area ◽  
Specific Surface Area ◽  
Heteropoly Acid ◽  
Mercury Intrusion Porosimetry ◽  
Fractal Dimensions ◽  
Surface Fractal Dimension ◽  
Mercury Intrusion ◽  
Surface Fractal

Experimental adsorption isotherms were used to evaluate the specific surface area and the surface fractal dimensions of acid-activated bentonite samples modified with a heteropoly acid (HPW). The aim of the investigations was to search for correlations between the specific surface area and the geometric heterogeneity, as characterized by the surface fractal dimension and the content of added acid. In addition, mercury intrusion was employed to evaluate the porous microstructures of these materials. The results from the Frankel-Halsey-Hill method showed that, in the p/p0 region from 0.75 to 0.96, surface fractal dimension increased with increasing content of heteropoly acid. The results from mercury intrusion porosimetry (MIP) data showed the generation of mesoporous structures with important topographical modifications, indicating an increase in the roughness (fractal geometry) of the surface of the solids as a consequence of the modification with the heteropoly acid. By comparison, MIP is preferable for the characterization because of its wide effective probing range.

scholarly journals Morphology and fractal dimension of TiO2 thin films

2013 ◽  
Vol 32 (1) ◽  
pp. 309 ◽  
Author(s):  
Srdjan P Petrović
Keyword(s):  
Thin Films ◽  
Fractal Dimension ◽  
Annealing Temperature ◽  
Spray Deposition ◽  
Fractal Dimensions ◽  
Deposition Process ◽  
Tio2 Films ◽  
Surface Fractal ◽  
Different Temperatures ◽  
Afm Micrographs

The influence of annealing temperature on the morphology and surface fractal dimension of titanium dioxide (TiO2) films prepared via the spray deposition process was investigated. Thin films with various morphologies were obtained at different temperatures and characterized by X-ray diffraction and atomic force microscopy (AFM). It was found that the crystalline structure of TiO2 films depends strongly on annealing temperature. At higher temperatures, the partial phase transformation of anatase-to-rutile was observed. The morphology and surface fractal dimensions were evaluated by image analysis methods based on AFM micrographs. The results indicate that the value of surface roughness (the standard deviation of the height values within the given area of AFM image) of TiO2 films increases with increasing annealing temperature. Fractal analysis revealed that the value of the fractal dimension of the samples decreases slowly from 2.23 to 2.15 following the annealing process.  

scholarly journals Relevance of coral geometry in the outcomes of the coral-algal benthic war

2018 ◽  
Author(s):  
Emma E. George ◽  
James Mullinix ◽  
Fanwei Meng ◽  
Barbara Bailey ◽  
Clinton Edwards ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Surface Area ◽  
Essential Element ◽  
Fractal Dimensions ◽  
Environmental Conservation ◽  
Microbial Composition ◽  
Surface Area Ratio ◽  
Surface Fractal Dimension ◽  
Surface Fractal ◽  
The Mean

AbstractCorals have built reefs on the benthos for millennia, becoming an essential element in marine ecosystems. Climate change and human impact, however, are favoring the invasion of non-calcifying benthic algae and reducing coral coverage. Corals rely on energy derived from photosynthesis and heterotrophic feeding, which depends on their surface area, to defend their outer perimeter. But the relation between geometric properties of corals and the outcome of competitive coral-algal interactions is not well known. To address this, 50 coral colonies interacting with algae were sampled in the Caribbean island of Curaçao. 3D and 2D digital models of corals were reconstructed to measure their surface area, perimeter, and polyp sizes. A box counting algorithm was applied to calculate their fractal dimension. The perimeter and surface dimensions were statistically non-fractal, but differences in the mean surface fractal dimension captured relevant features in the structure of corals. The mean fractal dimension and surface area were negatively correlated with the percentage of losing perimeter and positively correlated with the percentage of winning perimeter. The combination of coral perimeter, mean surface fractal dimension, and coral species explained 19% of the variability of losing regions, while the surface area, perimeter, and perimeter-to-surface area ratio explained 27% of the variability of winning regions. Corals with surface fractal dimensions smaller than two and small perimeters displayed the highest percentage of losing perimeter, while corals with large surface areas and low perimeter-to-surface ratios displayed the largest percentage of winning perimeter. This study confirms the importance of fractal surface dimension, surface area, and perimeter of corals in coral-algal interactions. In combination with non-geometrical measurements such as microbial composition, this approach could facilitate environmental conservation and restoration efforts on coral reefs.

DISTINCT FRACTAL CHARACTERISTICS OF MONOMER AND MULTIMER PROTEINS

Fractals ◽  
2010 ◽  
Vol 18 (02) ◽  
pp. 207-214 ◽  
Author(s):  
DANA CRACIUN ◽  
ADRIANA ISVORAN ◽  
R. D. REISZ ◽  
N. M. AVRAM
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Structural Characteristics ◽  
Fractal Dimensions ◽  
The Other ◽  
Mean Values ◽  
Surface Fractal Dimension ◽  
Surface Fractal ◽  
Fractal Characteristics ◽  
The Mean

Within this study we have calculated the surface fractal dimension (Ds) and the backbone fractal dimensions associated to the local folding (D1) and to the global folding (D2) for two unbiased sets of 50 proteins each, one for monomer and the other for homo- multimer proteins. The mean surface fractal dimension is Ds = 2.29 ± 0.02 for monomers and Ds = 2.21 ± 0.01 for multimers, the two means being significantly different. The mean backbone fractal dimensions associated to the local folding are D1 = 1.34 ± 0.14 for monomers and D1 = 1.33 ± 0.11 for multimers and those associated to the global folding are D2 = 1.33 ± 0.05 for monomers and D2 = 1.29 ± 0.04 for multimers, respectively. There are not significant differences between the mean values of the backbone fractal dimensions corresponding to monomers and multimers. These results suggest that there are different structural characteristics between monomer and multimer proteins only concerning their surface roughness, with multimers being smoother than monomers.

scholarly journals Skin Lesion Classification Based on Surface Fractal Dimensions and Statistical Color Cluster Features Using an Ensemble of Machine Learning Techniques

Cancers ◽  
2021 ◽  
Vol 13 (21) ◽  
pp. 5256
Author(s):  
Simona Moldovanu ◽  
Felicia Anisoara Damian Michis ◽  
Keka C. Biswas ◽  
Anisia Culea-Florescu ◽  
Luminita Moraru
Keyword(s):  
Neural Network ◽  
Fractal Dimension ◽  
Skin Cancer ◽  
Skin Lesion ◽  
Fractal Dimensions ◽  
Color Distribution ◽  
Surface Fractal Dimension ◽  
Color Features ◽  
Surface Fractal ◽  
Lesion Classification

(1) Background: An approach for skin cancer recognition and classification by implementation of a novel combination of features and two classifiers, as an auxiliary diagnostic method, is proposed. (2) Methods: The predictions are made by k-nearest neighbor with a 5-fold cross validation algorithm and a neural network model to assist dermatologists in the diagnosis of cancerous skin lesions. As a main contribution, this work proposes a descriptor that combines skin surface fractal dimension and relevant color area features for skin lesion classification purposes. The surface fractal dimension is computed using a 2D generalization of Higuchi’s method. A clustering method allows for the selection of the relevant color distribution in skin lesion images by determining the average percentage of color areas within the nevi and melanoma lesion areas. In a classification stage, the Higuchi fractal dimensions (HFDs) and the color features are classified, separately, using a kNN-CV algorithm. In addition, these features are prototypes for a Radial basis function neural network (RBFNN) classifier. The efficiency of our algorithms was verified by utilizing images belonging to the 7-Point, Med-Node, and PH2 databases; (3) Results: Experimental results show that the accuracy of the proposed RBFNN model in skin cancer classification is 95.42% for 7-Point, 94.71% for Med-Node, and 94.88% for PH2, which are all significantly better than that of the kNN algorithm. (4) Conclusions: 2D Higuchi’s surface fractal features have not been previously used for skin lesion classification purpose. We used fractal features further correlated to color features to create a RBFNN classifier that provides high accuracies of classification.

FRACTAL DIMENSION, PRIMES, AND THE PERSISTENCE OF MEMORY

2003 ◽  
Vol 06 (02) ◽  
pp. 241-249
Author(s):  
JOSEPH L. PE
Keyword(s):  
Number Theory ◽  
Fractal Dimension ◽  
Fractal Dimensions ◽  
Distinguishing Characteristic ◽  
Local Behavior ◽  
Remarkable Similarity ◽  
Recursive Procedures

Many sequences from number theory, such as the primes, are defined by recursive procedures, often leading to complex local behavior, but also to graphical similarity on different scales — a property that can be analyzed by fractal dimension. This paper computes sample fractal dimensions from the graphs of some number-theoretic functions. It argues for the usefulness of empirical fractal dimension as a distinguishing characteristic of the graph. Also, it notes a remarkable similarity between two apparently unrelated sequences: the persistence of a number, and the memory of a prime. This similarity is quantified using fractal dimension.

Sign in / Sign up

Export Citation Format

Share Document